6

Part of 2007 Portugal MO

Problems(1)

M/m >= \sqrt3 for 6 houses with min /max distances 2007 Portugal p6

Source:

In a village, the maximum distance between two houses is

M

and the minimum distance is

m

. Prove that if the village has

6

\frac{M}{m} \ge \sqrt3

geometryminmaxdistance